Quantum computer

ABSTRACT

A quantum computer comprising a semiconductor substrate into which donor atoms are introduced to produce an array of donor nuclear spin electron systems having large electron wave functions at the nucleus of the donor atoms, where the donor electrons only occupy the nondegenerate lowest spin energy level. An insulating layer above the substrate. Conducting A-gates on the insulating layer above respective donor atoms to control strength of the hyperfine interactions between the donated electrons and the donor atoms&#39; nuclear spins, and hence the resonance frequency of the nuclear spins of the donor atoms. Conducting J-gates on the Insulating layer between the A-gates to turn on and off electron mediated coupling between the nuclear spins or adjacent donor atoms. Where the nuclear spins of the donor atoms are the quantum states or “qubits” in which binary information is stored and manipulated by selective application of voltage to the A- and J-gates and selective application of an alternating magnetic field to the substrate.

TECHNICAL FIELD

This invention concerns a quantum computer, that is a device forperforming quantum computations. Recent progress in the theory ofquantum computation, particularly the discovery of fast quantumalgorithms, makes the development of such a device an importantpriority.

BACKGROUND ART

Finding an approach to quantum computation that fulfils the requirementshas proved to be a formidable challenge. Nuclear spins have beenincorporated into quantum computer proposals, because their lifetime canbe at least six orders of magnitude greater than the time required toperform a logical operation on the spins.

SUMMARY OF THE INVENTION

The invention is a quantum computer, including:

A semiconductor substrate into which donor atoms are introduced toproduce an array of donor nuclear spin electron systems having largeelectron wave functions at the nucleus of the donor atoms. Where thedonor electrons (electrons weakly bound to the donor atom) only occupythe nondegenerate lowest spin energy level.

An insulating layer above the substrate.

Conducting A-gates on the insulating layer above respective donor atomsto control the strength of the hyperfine interactions between the donorelectrons and the donor atoms' nuclear spins, and hence the resonancefrequency of the nuclear spins of the donor atoms.

Conducting J-gates on the insulating layer between A-gates to turn onand off electron mediated coupling between the nuclear spins of adjacentdonor atoms.

Where, the nuclear spins of the donor atoms are the quantum states or“qubits” in which binary information is stored and manipulated byselective application of voltage to the A- and J-gates and selectiveapplication of alternating magnetic field to the substrate.

A cooling means may be required to maintain the substrate cooled to atemperature sufficiently low, and a source of constant magnetic fieldhaving sufficient strength to break the two-fold spin degeneracy of thebound state of the electron at the donor may also be required. Thecombination of cooling and magnetic field may be required to ensure theelectrons only occupy the nondegenerate lowest spin energy level.

The device may also incorporate a source of alternating magnetic fieldof sufficient force to flip the nuclear spin of donor atoms resonantwith the field, and means may be provided to selectively apply thealternating magnetic field to the substrate.

In addition the device may include means to selectively apply voltage tothe A-gates and J-gates.

The invention takes advantage of the fact that an electron is sensitiveto externally applied electric fields. As a result the hyperfineinteraction between an electron spin and the spin of the atomic nucleus,and the interaction between an electron and the nuclear spins of twoatomic nuclei (that is electron mediated or indirect nuclear spincoupling) can be controlled electronically by voltages applied to gateson a semiconductor device in the presence of an alternating magneticfield. The invention uses these effects to externally manipulate thenuclear spin dynamics of donor atoms in a semiconductor for quantumcomputation.

In such a device the lifetime of the quantum states (or qubits) operatedon during the computation must exceed the duration of the computation,otherwise the coherent state within the computer upon which quantumalgorithms rely will be destroyed. The conditions required forelectron-coupled nuclear spin computation and single nuclear spindetection can arise if the nuclear spin is located on a positivelycharged donor in a semiconductor host. The electron wave function isthen concentrated at the donor nucleus (for s-orbitals and energy bandscomposed primarily of them), yielding a large hyperfine interactionenergy. For shallow level donors, however, the electron wave functionextends tens or hundreds of Å away from the donor nucleus, allowingelectron-mediated nuclear spin coupling to occur over comparabledistances.

An important requirement for a quantum computer is to isolate the qubitsfrom any degrees of freedom that may interact with and “decohere” thequbits. If the qubits are spins on a donor in a semiconductor, thennuclear spins in the host are a large reservoir with which the donorspins can interact. Consequently, the host should contain only nucleiwith spin I=0. This requirement eliminates all III-V semiconductors ashost candidates, since none of their constituent elements possess stableI=0 isotopes. Group IV semiconductors are composed primarily of I=0isotopes and may be purified to contain only I=0 isotopes. Because ofthe advanced state of Si materials technology and the tremendous effortcurrently underway in Si nanofabrication, Si is an attractive choice forthe semiconductor host.

The only I=½ shallow (Group V) donor in Si is ³¹P. The Si:³¹P system wasexhaustively studied forty years ago by Feher in the firstelectron-nuclear double resonance experiments. At sufficiently low ³¹pconcentrations at temperature T=1.5 K, Feher observed that the electronrelaxation time was thousands of seconds and the ³¹P nuclear relaxationtime exceeded 10 hours. At millikelvin temperatures the phonon limited³¹P relaxation time may be of order 10¹⁸ seconds, making this systemideal for quantum computation.

The A- and J-gates may be formed from metallic strips patterned on thesurface of the insulating layer. A step in the insulating layer overwhich the gates cross may serve to localise the gates electric fields inthe vicinity of the donor atoms.

In operation the temperature of the quantum computer may be below 100millikelvin (mK) and will typically be in the region of 50 mK. Theprocess of quantum computation is non-dissipative, and consequently lowtemperatures can be maintained during computation with comparative ease.Dissipation will arise external to the computer from gate biasing andfrom eddy currents caused by the alternating magnetic field, and duringpolarisation and detection of nuclear spins at the beginning and end ofthe computation. These effects will determine the minimum operabletemperature of the computer.

The constant magnetic field may be required to be of the order of 2Tesla. Such powerful magnetic fields may be generated fromsuperconductors.

The extreme temperatures and magnetic fields required impose somerestrictions on the availability and portability of the quantumcomputing device outside of a laboratory. However, the high level ofaccess to a computer situated remotely in a laboratory, for instancethrough use of the internet, may overcome any inconvenience arising fromits remoteness. It is also feasible that the device could be utilised asa network server for personal computers, in which case the server mayhave a local cooling system and the personal computers may operate atroom temperature.

The initial state of the computer must be accurately set and the resultof the computation accurately measured. Electron devices may be providedto set the initial state and read output from the quantum computer.These devices polarize and measure nuclear spins. For example, theelectron device may modulate the movement of a single electron, or acurrent of electrons, according to the state of a single nuclear spin.These devices will typically be provided at the edge of the array.

An electron device for polarizing and measuring nuclear spins may,comprise:

A semiconductor substrate into which at least one donor atom isintroduced to produce a donor nuclear spin electron system having largeelectron wave functions at the nucleus of the donor atom.

An insulating layer above the substrate.

A conducting A-gate on the insulating layer above the donor atom tocontrol the energy of the bound electron state at the donor.

A conducting E-gate on the insulating layer on either side of the A-gateto pull electrons into the vicinity of the donor.

Where in use, the gates are biased so that, if the transition isallowed, one or more electrons can interact with the donor state.

In a further aspect, the invention is a method of initializing thequantum computer, comprising the following steps:

biasing the gates so that, if the nuclear spin of a donor is in a firststate no transition is allowed, but if the nuclear spin is in a secondstate transition is allowed, and one or more electrons can interact withthe donor state to change the nuclear spin to the first state; and

continuing the process until all the donors are in the first state.

In a further aspect, the invention is a method of measuring nuclearspins in the quantum computer, comprising the following steps:

biasing the gates so that, if the nuclear spin of a donor is in a firststate no transition is allowed, but if the nuclear spin is in a secondstate transition is allowed, and one or more electrons can interact withthe donor state to change the nuclear spin to the first state; and

detecting the movement of the one or more electrons to determine thestate of the respective donors.

BRIEF DESCRIPTION OF THE DRAWINGS

An example of the invention will now be described with reference to theaccompanying drawings, in which:

FIG. 1 illustrates two cells in a 1-Dimensional array containing ³¹Pdonors and electrons in a Si host, separated by a barrier from metalgates on the surface. A-gates control the resonance frequency of thenuclear spin qubits, while J-gates control the electron-mediatedcoupling between adjacent nuclear spins. The ledge over which the gatescross localises the gate electric field in the vicinity of the donors.

FIG. 2 illustrates how an electric field applied to an A-gate pulls theelectron wave function away from the donor atom and toward the barrier,reducing the hyperfine interaction and the resonance frequency of thenucleus. The donor nuclear spin electron system acts as a voltagecontrolled oscillator.

FIG. 3 illustrates how an electric field applied to a J-gate varies theelectrostatic potential barrier V between the donors to enhance orreduce the exchange coupling, proportional to the electron wave functionoverlap. The exchange frequency (=4J/h) when V=0 is plotted for Si.

FIG. 4 illustrates the effect on electron and nuclear spin energies whenJ coupling is turned on. In FIG. 4(a) the exchange interaction lowersthe electron singlet energy with respect to the triplets. The computeris always operated when J<μ_(B)B/2 so that the electron state is spinpolarised. In FIG. 4(b) nuclear level splitting can be seen due toelectron mediated interactions between the nuclei; the |10−01>−|10+01>splitting diverges (in second order perturbation theory) whenJ=μ_(B)B/2.

FIG. 5 (a), (b) and (c) illustrates a controlled NOT operation, realisedby adiabatic variations in J, Δ_(A), and B_(AC).

FIG. 6 illustrates a configuration at the edge of the array forpolarising and detecting nuclear spins. FIG. 6(a) is a pictorial view ofthe arrangement When positively biased, E-gates pull electrons fromohmic contacts (not shown) into the vicinity of the edge qubit donor.FIG. 6(b) is a section showing the ³¹P donor weakly coupled to 2 DEG's;if the transition is allowed, an electron can tunnel through the donorstate. FIG. 6(c) illustrates the “spin diode” configuration, in whichelectron spin states at the Fermi level on opposite sides of the donorhave opposite polarity. Resonant tunnelling from one side to the otherwill flip the nuclear spin on the donor, so that the nuclear spin ispolarised by an electrical current. FIG. 6(d) illustrates the “singleelectron spin valve” configuration, in which electrons cannot tunnelonto the donor unless it can transfer its spin to the nucleus, resultingin a spin blockade if the electron and nuclear spins initially point inthe same direction. An electron traversing across the donor must flipthe nuclear spin twice, however, so the initial nuclear spinpolarisation is preserved.

BEST MODES FOR CARRYING OUT THE INVENTION

Referring first to FIG. 1 (not to scale), a 1-Dimensional array 1 havingtwo cells 2 and 3 comprises a Si substrate 4 into which two donor atoms5 and 6 of ³¹P are introduced 200 Å beneath the surface 7. There is oneatom of ³¹P in each cell and the atoms are separated by less than 200 Å.Conducting A-gates 8 are laid down on a SiO₂ insulating layer 9 abovethe Si substrate 4, each A-gate being directly above a respective ³¹Patom. Conducting J-gates 10 are laid down on the insulating layer 9between each cell 2 and 3. A step 11 over which the gates crosslocalises the gates electric fields in the vicinity of the donor atoms 5and 6.

The nuclear spins of the donor atoms 5 and 6 are the quantum states or“qubits” in which binary information is stored and manipulated. TheA-gates 8 control the resonance frequency of the nuclear spin qubits,while J-gates 10 control the electron-mediated coupling between adjacentnuclear spins.

In operation, the device is cooled to a temperature of T=50 mK. Also, aconstant magnetic field of B=2T is applied to break the two-fold spindegeneracy. The combined effect is that the electrons only occupy thenondegenerate lowest spin energy level. The electrons must remain in azero entropy ground state throughout a computation.

Magnitude of Spin Interactions in Si:³¹P

The size of the interactions between spins determines both the timerequired to do elementary operations on the qubits and the separationnecessary between donors in the array. The Hamiltonian for a nuclearspin-electron system in Si, applicable for an I=½ donor nucleus and withB°z is:

H _(en)=_(μB) Bσ _(z) ^(e)−g_(n)μ_(n) Bσ_(z) ^(n) +Aσ^(θ).σ^(n)

where σ are the Pauli spin matrices (with eigenvalues ±1), μ_(n) is thenuclear magneton, g_(n) is the nuclear g-factor (=1.13 for ³¹P), andA={fraction (8/3)}πμ_(B)g_(n)μ_(n)|Ψ(0)|² is the contact hyperfineinteraction energy, with |Ψ(0)|² the probability density of the electronwave function evaluated at the nucleus. If the electron is in its groundstate, the frequency separation of the nuclear levels is, to secondorder: $\begin{matrix}{{hv}_{A} = {{2g_{n}\mu_{n}B} + {2A} + \frac{2A^{2}}{\mu_{B}B}}} & (2)\end{matrix}$

In Si:³¹P, 2A/h=58 Mhz, and the second term in Equation (2) exceeds thefirst term for B<3.5 T.

An electric field applied at the A-gate to the electron-donor systemshifts the electron wave function envelope away from the nucleus andreduces the hyperfine interaction. The size of this shallow donor Starkshift in Si, is shown in FIG. 2 for a donor 200 Å beneath a gate. Adonor nuclear spin-electron system close to an A-gate functions as avoltage controlled oscillator: the precession frequency of the nuclearspin can be controlled externally, and spins can be selectively broughtinto resonance with an externally applied alternating magnetic field,B_(AC)=10⁻³ T, allowing arbitrary rotations to be performed on thenuclear spin.

Quantum mechanical computation requires, in addition to single spinrotations, the two qubit “controlled rotation” operation, which rotatesthe spin of a target qubit through a prescribed angle if and only if thecontrol qubit is oriented in a specified direction, and leaves theorientation of the control qubit unchanged. Performing such two spinoperations requires coupling between two donor-electron spin systems,which will arise from the electron spin exchange interaction when thedonors are sufficiently close to each other. The Hamiltonian of twocoupled donor nuclei-electron systems is:

 H=H(B)+A ₁σ^(1n). σ^(1e) +A ₂σ^(2n). σ^(2e) +Jσ ^(1e). σ^(2e)  (3)

where H(B) are the magnetic field interaction terms for the spins. A₁and A₂ are the hyperfine interaction energies of the nucleus-electronsystems. 4J, the exchange energy, depends on the overlap of the electronwave functions. For well separated donors:${4{J(r)}} \cong {1.6\frac{e^{2}}{\varepsilon \quad a_{B}}( \frac{r}{a_{B}} )^{\frac{5}{2}}{\exp ( \frac{{- 2}r}{a_{B}} )}}$

where r is the distance between donors ∈ is the dielectric constant ofthe semiconductor, and α_(B) is the semiconductor Bohr radius. Thisfunction, with values appropriate for Si, is plotted in FIG. 3. Equation4, originally derived for H atoms, is complicated in Si by its valleydegenerate anisotropic band structure. Exchange coupling terms from eachvalley interfere, leading to oscillatory behaviour of J(r). In thisexample the complications introduced by Si band structure are neglected.In determining J(r) in FIG. 3, the transverse mass for Si(≅0.2 m_(e))has been used, and α_(B)=30 Å. As shall be seen below, significantcoupling between nuclei will occur when 4J≈μ_(B)B, and this conditiondetermines the necessary separation between donors of 100-200 Å. BecauseJ is proportional to the electron wave function overlap, it can bevaried by an electrostatic potential imposed by a J-gate positionedbetween the donors.

For two electron systems the exchange interaction lowers the electronsinglet (|↑↓−↓↑>) energy with respect to the triplets. In a magneticfield, however, the electron ground state will be polarised ifμ_(B)B>2J; see FIG. 4a. In the polarised ground state, the energies ofthe nuclear states can be calculated to second order in A usingperturbation theory. The nuclear singlet (|10−01>) is lowered in energywith respect to (|10+01>) by: $\begin{matrix}{{hv}_{j} = {2{A^{2}( {\frac{1}{{\mu_{B}B} - {2J}} - \frac{1}{\mu_{B}B}} )}}} & (5)\end{matrix}$

The other two triplet states are higher and lower than these states byhv_(A), given in Equation 2; see FIG. 4b. For the Si:³¹P system at B=2Tesla and for 4J/h=30 Ghz, Equation 5 yields v_(i)=75 kHz. Thisfrequency approximates the upper limit of the rate at which binaryoperations can be performed on the computer. The speed of single spinoperations is determined by the size of B_(AC) and is comparable to 75kHz when B_(AC)=10⁻³ Tesla.

Equation 5 was derived for A₁=A₂. When A₁≠A₂ the nuclear spin singletsand triplets are no longer eigenstates, and the eigenstates of thecentral levels will approach |10> and |01> when |A₁−A₂|>>hv_(j), as ischaracteristic of two level systems; see FIG. 5a.

Control of the J-gates, combined with control of A-gates and applicationof B_(AC), are sufficient to effect the controlled rotation operationbetween two adjacent spins.

The controlled NOT operation (conditional rotation of the target spin by180°) can be performed using an adiabatic procedure, in which the gatebiases are swept slowly; refer to FIGS. 5b & c. At t=t₀, the two spinsystems are uncoupled (J=0) and A₁=A₂ so that |10> and |01> aredegenerate. At t₁ a differential voltage is applied to the A-gates(designated Δ_(A)) that breaks this degeneracy. This symmetry breakingstep distinguishes the control qubit from the target qubit. At t₂exchange coupling between the spin systems is turned on, and at t₃ theΔ_(A) bias is removed. This sequence of steps adiabatically evolves |01>into |10−01> and |10> into |10+01>. At t₄ B_(AC) is applied resonantwith the |10+01>−|11> energy gap. Although to lowest order inperturbation theory, B_(AC) will also be resonant with the |00>−|10−01>gap, the matrix element of this second transition is zero since thesinglet state is not coupled to the other states by B_(AC).

B_(AC) is left on until t₅, when it has transformed |11> into |10+01>and vice versa. The |10−01> and |10+01> are then adiabaticallytransformed back into |10> and |01> in a reverse of the sequence ofsteps performed at the beginning of the operation. The qubit whoseresonance energy was increased by the action of Δ_(Λ) at the outset isunchanged, while the state whose energy was decreased is inverted if andonly if the other qubit is |1>. The controlled NOT operation has beenperformed. Arbitrary controlled rotations can be accomplished byappropriately setting the duration and frequency of B_(AC).

It is likely that computational steps can be performed more efficientlythan the adiabatic approach discussed above allows. In particular, theEXCHANGE operation (in which adjacent qubits are simply swapped with oneanother, the only way the qubits can be moved around in a quantumcomputer) can be effected by turning on a J-gate when Δ_(A)=0 for aperiod=v_(f) ⁻¹/2. Also, B_(AC) can be continuously on and the qubitsbrought into resonance with it during the controlled NOT operation byvarying A₁+A₂=Σ_(A) of the coupled spins. This approach enables unaryand binary operations to be performed on qubits throughout the computersimultaneously, with the nature of the operation on each qubitdetermined entirely by the individual A-gate and J-gate biases.

Spin Decoherence Introduced by Gates

In the quantum computer architecture outlined above, biasing of A-gatesand J-gates enables custom control of the qubits and their mutualinteractions. The presence of the gates, however, will lead todecoherence of the spins if the gate biases fluctuate away from theirdesired values. The largest source of decoherence is likely to rise fromvoltage fluctuations on the A-gates. The precession frequencies of twospins in phase at t=0 depends on the potentials on their respectiveA-gates, Differential fluctuations of the potentials produce differencesin the precession frequency. At some later time t=t_(φ) the spins willbe 180° out of phase. t_(φ) can be estimated by determining thetransition rate between |10+01> (spins in phase) and |10−01> (spins 180°out of phase) of a two spin system. The Hamiltonian that couples thesestates is: $\begin{matrix}{H_{\varphi} = {\frac{1}{4}h\quad {\Delta ( {\sigma_{2}^{1n} - \sigma_{2}^{2n}} )}}} & (6)\end{matrix}$

where Δ is the fluctuating differential precession frequency of thespins. Standard treatment of fluctuating Hamiltonians predicts: t_(φ)⁻¹=π²S_(Δ)(v_(st)), where S_(Δ) is the spectral density of the frequencyfluctuations, and v_(st) is the frequency difference between the |10−01>and |10+01>states. At a particular bias voltage, the A-gates have afrequency tuning parameter α=dΔ/dV. Thus:

 t _(φ) ⁻¹=π²α²(V)S _(V)(ν_(st)),  (7)

where S_(v) is the spectral density of the gate bias potentialfluctuations.

S_(v) for good room temperature electronics is of order 10⁻¹⁸V²/Hz,comparable to the room temperature Johnson noise of a 50Ω resistor, α,estimated from FIG. 2, is 10-100 MHz/Volt, yielding t_(φ)=10-1000 sec. αis determined by the size of the donor array cells and cannot readily bereduced (to increase t_(φ)) without reducing the exchange interactionbetween cells. Because α is a function of the gate bias (see FIG. 2)t_(φ) can be increased by minimising the voltage applied to the A-gates.

While Equation 7 is valid for white noise, at low frequencies it islikely that materials dependent fluctuations (1/f noise) will be thedominant cause of spin dephasing. Consequently, it is difficult to givehard estimates of t_(φ) for the computer. A particular source of lowfrequency fluctuations, alluded to above, arises from nuclear spins inthe semiconductor host. This source of spin dephasing can be eliminatedby using only I=0 isotopes in the semiconductor and barrier layers.Charge fluctuations within the computer (arising from fluctuatingoccupancies of traps and surface states, for example) are likely to beparticularly important, and minimising them will place great demands oncomputer fabrication.

While material dependent fluctuations are difficult to estimate, the lowtemperature operation of the computer and the dissipationless nature ofquantum computing mean that in principle fluctuations can be keptextremely small: using low temperature electronics to bias the gatescould produce t_(φ)≈10⁶ sec. Electronically controlled nuclear spinquantum computers thus have the theoretical capability to perform atleast 10⁵ to perhaps 10¹⁰ logical operations during t_(φ), a criticalrequirement for performing complex calculations on large numbers ofqubits.

Spin lnitialisation and Measurement

The action of A-gates and J-gates, together with B_(AC) perform all ofthe reversible operations for quantum computation. The qubits must alsobe properly initialised and measured.

To accomplish these tasks in the proposed computer, qubits at the edgeof the array are weakly coupled to two dimensional electron gases (2DEG's) that are confined to the barrier-Si interface by a positivepotential on E-gates (a field effect transistor in enhancement mode);see FIG. 6a. The nuclear spin qubit is probed by an electron tunnellingthrough a bound state at the donor; see FIG. 6b. When B≠0 the electronenergy levels are discrete and electron spin levels are split by 2μ_(B)B. When the Landau level filling factor v<1, the electron spins arecompletely polarised at low temperature. When v>1, however, electronsmust occupy the higher 10 energy spin level and states at the Fermilevel (E_(F)) are polarised in the opposite direction than for v<1 (Forsimplicity, neglecting the valley degeneracy of the electrons in Si.Also, many body “skyrmion” effects that can reduce the electron spinpolarisation are small in Si and are also neglected).

A junction between a v<1 region and a v>1 region is a “spin diode”, socalled because of the analogy between electron spin splitting in thesedevices and the band gap in a semiconductor p-n junction diode; see FIG.6c. Spin diodes are created by biasing the two E-gates at differentvoltages that produce different densities in each 2 DEG. The largeenergy difference between electron and nuclear spin flip energiesusually impedes spin transfer, but the electric field in the spin diodejunction enables |↑> and |↓> states of the electron with the same energyto overlap, enabling resonant electron-nuclear spin exchange. Thenucleus in the junction can thus be polarised rapidly by a currentthrough the junction. |0> qubit states created in this way at the edgesof the donor array can be transferred throughout the array by theEXCHANGE operation. |0>'s can be converted into |1>'s with selectiveunary NOT operations to complete the initialisation procedure.

Fluctuations from cell to cell in the gate biases necessary to performlogical operations are an inevitable consequence of variations in thepositions of the donors and in the sizes of the gates. The parameters ofeach cell, however, can be determined individually using the measurementcapabilities of the computer, because the measurement techniquediscussed here does not require precise knowledge of the J and Acouplings. The A-gate voltage at which the underlying nuclear spin isresonant with an applied B_(ac) can be determined using the technique ofadiabatic fast passage: when B_(ac)=0, the nuclear spin is measured andthe A-gate is biased at a voltage known to be off resonance. B_(ac) isthen switched on, and the A-gate bias is swept through a prescribedvoltage interval. B_(ac) is then switched off and the nuclear spin ismeasured again. The spin will have flipped if, and only if, resonanceoccurred within the prescribed A-gate voltage range. Testing for spinflips in increasingly small voltage ranges leads to the determination ofthe resonance voltage. Once adjacent A-gates have been calibrated, theJ-gates can be calibrated in a similar manner by sweeping J-gate biasesacross resonances of two coupled cells.

Instead of using the EXCHANGE operation, the calibration procedure 10can be performed in parallel on many cells, and the calibration voltagescan be stored on capacitors located on the Si chip adjacent to thequantum computer to initialize it. Calibration is not a fundamentalimpediment to scaling the computer to large sizes, and externalcontrolling circuitry would thus need to control only the timing of gatebiases, and not their magnitudes.

Readout of the nuclear spin state can be performed simply by reversingthe loading process. Since electrons can only traverse a spin diodejunction by exchanging spin with a nucleus (say, by converting |1> into|0>) a “spin blockade” will result if the nuclear spin is |0>. If thenuclear state is |1>, a single electron can cross the junction,simultaneously flipping the nucleus from |1> to |0>.

Because a |1> state is converted to a single electron crossing thejunction, this detection technique requires extremely sensitive singleelectron sensing circuitry. It would be preferable to have a conductancemodulation technique to sense the nuclear spin. If large numbers ofelectrons can interact with the nuclear spin without depolarising it,many separate effective measurements could be made of the spin.

One possibility is the “single electron spin valve” configuration shownin FIG. 6d. The E-gates are biased so that only |↓> electrons arepresent on both sides of the output cell. The A-gate of the output cellis biased so that E_(F) lies at the energy of the two electron boundstates at the donor (the D⁻ state). In Si:³¹ P at B=2 Tesla this stateis a singlet, and the second electron binding energy is 1.7 meV, aboutseven times greater than the spin level splitting. In a single electronspin valve an electron can tunnel on or off of the D⁻ state by a mutualelectron-nuclear spin flip only if the nuclear and electron spins areoppositely polarised. A current flow across the donor requires twosuccessive spin flips as the electron tunnels in and out of the D⁻state,consequently, a current across the donor preserves the nuclear spinpolarisation. Current flow across the single electron spin valve isturned on or off depending on the orientation of the nuclear spin on thedonor.

The rate of electron transmission across a single electron spin valvecan potentially be comparable to the hyperfine interaction frequency: 60MHz in Si:³¹ P, or I=10 pA. In actual devices a background current ofelectrons tunnelling through channels that do not flip the nuclear spinwill inevitably be present. Dipolar spin interactions (generally muchweaker that the contact hyperfine interaction) can flip a single nuclearspin without an accompanying electron spin flip, and will limit thenumber of electrons that can probe the nuclear spin before it isdepolarised. Optimised devices will maximise the ratio of the number ofelectrons that can probe the nucleus to the background. Prototype singleelectron spin valve devices can be tested using single electroncapacitance probes of donor states with nonzero nuclear spin.

Constructing the Computer

The materials used to build such a computer must be almost completelyfree of spin (I=/0 isotopes) and charge impurities in order to preventdephasing fluctuations from arising within the computer. Donors must beintroduced into the material in an ordered array hundreds of Å beneaththe surface. Finally, the gates with lateral dimensions and separations<100 Å must be patterned on the surface, registered to the donorsbeneath them. Each of these are the focus of intense current research inthe rapidly moving field of semiconductor growth and nanofabrication.This research bears directly on the problems of making a nuclear spinquantum computer in silicon.

An excellent indicator of suitable semiconductor materials for use in aquantum computer is the ability to observe the integral and fractionalquantum Hall effects in them. In particular, the spin detectiontechniques outlined above require that electrons can be fully spinpolarised, a condition which leads to quantisation of the Hall effect atintegers corresponding to the spin gap. This condition is well satisfiedin high mobility GaAs/Al_(x)Ga_(1−x)As heterostructures, where nuclearspin sensing electronics have been demonstrated. Absence of I=0isotopes, however, in these materials means that making a quantumcomputer from them is highly unlikely. Recent advances inSi/Si_(x)Ge_(1−x) heterostructures have led to materials composedentirely of group IV elements with quality comparable to GaAsheterostructures. The fractional quantum Hall effect is observed inthese materials and spin splitting is well resolved. Nanostructures havealso been fabricated on high quality Si/Si_(x)Ge_(1−x) heterostructures.

While the quality of Si/SiO₂ interfaces and the electron systemsconfined there is less than that of epitaxial interfaces, spinsplittings are well resolved at low temperatures. The much largerbarrier height in SiO₂ over Si/Si_(x)Ge_(1−x)(3.3V vs. ˜0.2 V) is acritical advantage in nanostructures with sizes of 100 Å or less.Leakage of electrons across the barrier material, resulting in theremoval of an electron from a donor state, is a source of decoherence inthe quantum computer not mentioned previously. Electrons consequentlymust not tunnel across the barrier during the computation. Also, theability of J-gates to vary the exchange interaction over a large dynamicrange will improve in devices with large barrier heights. Technologiesbeing developed for electronics applications may result in structureswith both the high interface quality of Si/Si_(x)Ge_(1−x) and the largertunnel barrier of SiO₂. Because of charge fluctuations and disorder, itis likely that bulk and interface states in SiO₂ will need to be reducedor eliminated if a quantum computer is to be fabricated using SiO₂.

The most obvious obstacle to building the quantum computer presentedabove is the incorporation of the donor array into the Si layer beneaththe barrier layer. Currently semiconductor heterostructures aredeposited layer by layer. The δ-doping technique produces donors lyingon a plane in the material, with the donors randomly distributed withinthe plane. The quantum computer envisioned requires that the donors beplaced into an ordered 1D or 2D array; furthermore, precisely one donormust be placed into each array cell, making it extremely difficult tocreate the array by using lithography and ion implantation or by focuseddeposition. Methods currently under development to place single atoms onsurfaces using ultra high vacuum scanning tunnelling microscopy arelikely candidates to be used to position the donor array. This approachhas been used to place Ga atoms on a Si surface. A challenge will be togrow high quality Si layers on the surface subsequent to placement ofthe donors.

Because the donors in the array must be <200 Å apart in order forexchange coupling between the electron spins to be significant, the gatedimensions must be <100 Å. In addition, the gates must be accuratelyregistered to the donors beneath them. Scanned probe lithographytechniques have the potential to sense the location of the donorsbeneath the surface prior to exposing the gate patterns on the surface.For example, a scanning near field optical microscope could be used todetect the photoluminescence characteristic of the P donors in awavelength range that does not expose photoresist. After P detection andproper positioning of the probe, the resist is exposed with a differentlight wavelength. “Custom patterning” of the gates may prove to benecessary to compensate for irregularities or defects in the placementof the donor array.

Probably the most attractive aspect of an Si based quantum computer isthat many of the technical challenges facing its development are similarto those facing the next generation of conventional electronics;consequently, tremendous efforts are already underway to overcome theseobstacles. This commonality raises the hope that the difficult task ofmaking large 2D arrays of qubit cells will one day be accomplished usingconventional Si electronics technology. A particular problem withscaling of the computer presented here is that inevitable differences atthe atomic level between qubit cells means that the appropriate biasesto apply to gates during quantum computation will differ from cell tocell. Scaling the computer to large numbers of qubits will consequentlyrequire an equally large number of connections to external electronicsto enable custom gate biasing. It is still possible that nontrivialquantum calculations (say on the 10³-10⁴ qubits necessary for quantumcomputers to exceed the capability of conventional computers in solvingthe prime factorisation problem) could be performed by doing logicaloperations on only a few qubits at a time and addressing each gateseparately using conventional FET multiplexing circuitry locatedadjacent to the quantum computer. This approach greatly simplifies thedesign and operation of the computer at the expense of foregoing itscapability to perform many quantum logical operations in parallel.

It will be appreciated by persons skilled in the art that numerousvariations and/or modifications may be made to the invention as shown inthe specific embodiments without departing from the spirit or scope ofthe invention as broadly described. The present embodiments are,therefore, to be considered in all respects as illustrative and notrestrictive.

What is claimed is:
 1. A quantum computer, including: a semiconductorsubstrate into which donor atoms are introduced to produce an array ofdonor nuclear spin electron systems having large electron wave functionsat the nucleus of the donor atoms, where the donor electrons only occupythe nondegenerate lowest spin energy level; an insulating layer abovethe substrate; conducting A-gates on the insulating layer aboverespective donor atoms to control the strength of the hyperfineinteractions between the donated electrons and the donor atoms' nuclearspins, and hence the resonance frequency of the nuclear spins of thedonor atoms; conducting J-gates on the insulating layer between A-gatesto turn on and off electron mediated coupling between the nuclear spinsof adjacent donor atoms; where, the nuclear spins of the donor atoms arethe quantum states or “qubits” in which binary information is stored andmanipulated by selective application of voltage to the A- and J-gatesand selective application of an alternating magnetic field to thesubstrate.
 2. A quantum computer according to claim 1, where the nuclearspin is located on a positively charged donor in a semiconductor host.3. A quantum computer according to claim 2, where the host contains onlynuclei with spin I=0.
 4. A quantum computer according to claim 3, wherethe host contains only Group IV semiconductors composed of I=0 isotopesor purified to contain only I=0 isotopes.
 5. A quantum computeraccording to claim 4, where Si is the semiconductor host.
 6. A quantumcomputer according to claim 5, where Si:³¹P is the host-donor system. 7.A quantum computer according to any preceding claim, where the A andJ-gates are formed from metallic strips patterned on the surface of theinsulating layer.
 8. A quantum computer according to claim 7, wherethere is a step in the insulating layer over which the gates cross tolocalise the gates electric fields in the vicinity of the donor atoms.9. A quantum computer according to claim 1, including means toselectively apply voltage to the A-gates and J-gates.
 10. A quantumcomputer according to claim 1, including a cooling means to maintain thesubstrate cooled.
 11. A quantum computer according to claim 10, where inoperation the temperature of the device is below 100 millikelvin (mK).12. A quantum computer according to claim 11, where in operation thetemperature of the device is about 50 mK.
 13. A quantum computeraccording to claim 1, including a source of constant magnetic fieldhaving sufficient strength to break the two-fold spin degeneracy of thebound state of the electron at the donor.
 14. A quantum computeraccording to claim 13, where the constant magnetic field is of the orderof 2 Tesla.
 15. A quantum computer according to claim 14, where theconstant magnetic field is generated from superconductors.
 16. A quantumcomputer according to claim 1, including a cooling means to maintain thesubstrate cooled and a source of constant magnetic field havingsufficient strength to break the two-fold spin degeneracy of the boundstate of the electron at the donor where the combination of cooling andconstant magnetic field ensures the electrons only occupy thenondegenerate lowest spin energy level.
 17. A quantum computer accordingto claim 1, where the device also incorporates a source of alternatingnagnetic filed of sufficient force to flip the nuclear spin of donoratoms resonant with the field, and means to selectively apply thealternating magnetic field to the substrate.
 18. A quantum computeraccording to claim 1, including electron devices which polarize andmeasure nuclear spins to set the initial state or to read output fromthe quantum computer, or both.
 19. A quantum computer according to claim18, where the electron devices operate such that a single nuclear spinmodulates a current of electrons.
 20. A quantum computer according toclaim 18 or 19, where the electron devices are provided at the edge ofthe array.
 21. A quantum computer according to claim 18, where eachelectron device comprises: a semiconductor substrate into which at leastone donor atom is introduced to produce a donor nuclear spin electronsystem having large electron wave functions at the nucleus of the donoratom; an insulating layer above the substrate; a conducting A-gate onthe insulating layer above the donor atom to control the strength of thehyperfine interaction between the donated electron and the donor atom'snuclear spin; and a conducting E-gate on the insulating layer on eitherside of the A-gate to pull electrons into the vicinity of the donor. 22.A method of initializing the quantum computer according to claim 1,comprising the following steps: biasing the gates to cause the nuclearspin of all the donor atoms to adopt the same state.
 23. A method ofinitializing the quantum computer according to claim 1, comprising thefollowing steps: biasing the gates; and detecting whether there ismovement of electrons associated with each donor atom to determine thestate of the respective donors.